This item is printed on demand - it takes 3-4 days longer - Neuware -Classically developed as a tool for partial differential equations, theanalysis of operators known as pseudodifferential analysis is here regardedas a possible help in questions of arithmetic. The operators which make upthe main subject of the book can be characterized in terms of congruencearithmetic.They enjoy a Eulerian structure, and are applied to the searchfor new conditions equivalent to the Riemann hypothesis. These consist inthe validity of certain parameter-dependent estimates for a class of Hermitianforms of finite rank. The Littlewood criterion, involving sums ofM�bius coefficients, and the Weil so-called explicit formula, which leads tohis positivity criterion, fit within this scheme, using in the first case Weyl'spseudodifferential calculus, in the second case Fuchs'.The book should beof interest to people looking for new possible approaches to the Riemannhypothesis, also to new perspectives on pseudodifferential analysis and onthe way it combines with modular form theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few exceptions,no previous acquaintance is necessary. 180 pp. Englisch.

N� de ref. del art�culo 9783319927060

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T�tulo

Pseudodifferential Methods in Number Theory

Editor

Springer International Publishing Jul 2018

Fecha de publicaci�n

2018

Idioma

Ingl�s

ISBN 10

331992706X

ISBN 13

9783319927060

Encuadernaci�n

Taschenbuch

Estado

Neu

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Sinopsis

Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of M�bius coefficients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'.

The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to newperspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary.

De la contraportada

Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of M�bius coeffcients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'.

The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to new perspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no diffculty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary.

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BuchWeltWeit Ludwig Meier e.K.
Germany

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